(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Is there an isomorphism from <R,+> to <R+,[tex]\times[/tex]> where [tex]\phi[/tex](r)=0.5[tex]^{r}[/tex] when r [tex]\in[/tex] R?

2. Relevant equations

For an isomorphism I know it is necessary to show there is a 1-1 and onto function. I am unsure if I can use the steps I am trying to use to show it is 1-1.

3. The attempt at a solution

For phi(r)=phi(s) I want to show r=s. Am I able to take the ln (or log?) of both sides to get ln(.05[tex]^{r}[/tex])=ln(0.5[tex]^{s}[/tex])? I am not sure which to use (ln or log) and where these logarithmic functions would be defined since for r=s, r and s are supposed to be real numbers.

Thanks for the help.

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# Homework Help: Isomorphism help

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